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Previous solution didn't convert input d to a date in GMT.
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Ashley
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The best I could come up with is msSinceEpoch[d_String]f[d_String] := Module[{do = DateObject[d, TimeZone -> "GMT"]}, 1000 * UnixTime@dUnixTime@DateObject@do + DateValue[d DateValue[DateObject@do, "Millisecond"]"Millisecond"]].

The best I could come up with is msSinceEpoch[d_String] := 1000 * UnixTime@d + DateValue[d, "Millisecond"].

The best I could come up with is f[d_String] := Module[{do = DateObject[d, TimeZone -> "GMT"]}, 1000 * UnixTime@DateObject@do + DateValue[DateObject@do, "Millisecond"]].

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Ashley
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The best I could come up with is msSinceEpoch[d_String] := 1000 * UnixTime@d + DateValue[d, "Millisecond"].